(x+9)(x-3)=(2x+2)(x-3)

Solution for (x+9)(x-3)=(2x+2)(x-3) equation:

(x+9)(x-3)=(2x+2)(x-3)

We move all terms to the left:

(x+9)(x-3)-((2x+2)(x-3))=0

We multiply parentheses ..

(+x^2-3x+9x-27)-((2x+2)(x-3))=0


We calculate terms in parentheses: -((2x+2)(x-3)), so:

(2x+2)(x-3)

We multiply parentheses ..

(+2x^2-6x+2x-6)

We get rid of parentheses

2x^2-6x+2x-6

We add all the numbers together, and all the variables

2x^2-4x-6

Back to the equation:

-(2x^2-4x-6)


We get rid of parentheses

x^2-2x^2-3x+9x+4x-27+6=0

We add all the numbers together, and all the variables

-1x^2+10x-21=0

a = -1; b = 10; c = -21;
Δ = b2-4ac
Δ = 102-4·(-1)·(-21)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*-1}=\frac{-6}{-2}
=+3
$